### Abstract

The spatial rock-scissors-paper game (or cyclic Lotka-Volterra system) is extended to study how the spatiotemporal patterns are affected by the rewired host lattice providing uniform number of neighbours (degree) at each site. On the square lattice this system exhibits a self-organizing pattern with equal concentration of the competing strategies (species). If the quenched background is constructed by substituting random links for the nearest-neighbour bonds of a square lattice then a limit cycle occurs when the portion of random links exceeds a threshold value. This transition can also be observed if the standard link is replaced temporarily by a random one with a probability P at each step of iteration. Above a second threshold value of P the amplitude of global oscillation increases with time and finally the system reaches one of the homogeneous (absorbing) states. In this case the results of Monte Carlo simulations are compared with the predictions of the dynamical cluster technique evaluating all the configuration probabilities on one-, two-, four- and six-site clusters.

Original language | English |
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Pages (from-to) | 2599-2609 |

Number of pages | 11 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 37 |

Issue number | 7 |

DOIs | |

Publication status | Published - Feb 20 2004 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Physics A: Mathematical and General*,

*37*(7), 2599-2609. https://doi.org/10.1088/0305-4470/37/7/006

**Rock-scissors-paper game on regular small-world networks.** / Szabó, G.; Szolnoki, A.; Izsák, Rudolf.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 37, no. 7, pp. 2599-2609. https://doi.org/10.1088/0305-4470/37/7/006

}

TY - JOUR

T1 - Rock-scissors-paper game on regular small-world networks

AU - Szabó, G.

AU - Szolnoki, A.

AU - Izsák, Rudolf

PY - 2004/2/20

Y1 - 2004/2/20

N2 - The spatial rock-scissors-paper game (or cyclic Lotka-Volterra system) is extended to study how the spatiotemporal patterns are affected by the rewired host lattice providing uniform number of neighbours (degree) at each site. On the square lattice this system exhibits a self-organizing pattern with equal concentration of the competing strategies (species). If the quenched background is constructed by substituting random links for the nearest-neighbour bonds of a square lattice then a limit cycle occurs when the portion of random links exceeds a threshold value. This transition can also be observed if the standard link is replaced temporarily by a random one with a probability P at each step of iteration. Above a second threshold value of P the amplitude of global oscillation increases with time and finally the system reaches one of the homogeneous (absorbing) states. In this case the results of Monte Carlo simulations are compared with the predictions of the dynamical cluster technique evaluating all the configuration probabilities on one-, two-, four- and six-site clusters.

AB - The spatial rock-scissors-paper game (or cyclic Lotka-Volterra system) is extended to study how the spatiotemporal patterns are affected by the rewired host lattice providing uniform number of neighbours (degree) at each site. On the square lattice this system exhibits a self-organizing pattern with equal concentration of the competing strategies (species). If the quenched background is constructed by substituting random links for the nearest-neighbour bonds of a square lattice then a limit cycle occurs when the portion of random links exceeds a threshold value. This transition can also be observed if the standard link is replaced temporarily by a random one with a probability P at each step of iteration. Above a second threshold value of P the amplitude of global oscillation increases with time and finally the system reaches one of the homogeneous (absorbing) states. In this case the results of Monte Carlo simulations are compared with the predictions of the dynamical cluster technique evaluating all the configuration probabilities on one-, two-, four- and six-site clusters.

UR - http://www.scopus.com/inward/record.url?scp=1342268335&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1342268335&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/37/7/006

DO - 10.1088/0305-4470/37/7/006

M3 - Article

AN - SCOPUS:1342268335

VL - 37

SP - 2599

EP - 2609

JO - Journal Physics D: Applied Physics

JF - Journal Physics D: Applied Physics

SN - 0022-3727

IS - 7

ER -